Robust Learning with Imperfect Privileged Information

In the learning using privileged information (LUPI) paradigm, example data cannot always be clean, while the gathered privileged information can be imperfect in practice. Here, imperfect privileged information can refer to auxiliary information that is not always accurate or perturbed by noise, or alternatively to incomplete privileged information, where privileged information is only available for part of the training data. Because of the lack of clear strategies for handling noise in example data and imperfect privileged information, existing learning using privileged information (LUPI) methods may encounter serious issues. Accordingly, in this paper, we propose a Robust SVM+ method to tackle imperfect data in LUPI. In order to make the SVM+ model robust to noise in example data and privileged information, Robust SVM+ maximizes the lower bound of the perturbations that may influence the judgement based on a rigorous theoretical analysis. Moreover, in order to deal with the incomplete privileged information, we use the available privileged information to help us in approximating the missing privileged information of training data. The optimization problem of the proposed method can be efficiently solved by employing a two-step alternating optimization strategy, based on iteratively deploying off-the-shelf quadratic programming solvers and the alternating direction method of multipliers (ADMM) technique. Comprehensive experiments on real-world datasets demonstrate the effectiveness of the proposed Robust SVM+ method in handling imperfect privileged information.